A number of methods are known whereby moist textiles are bleached during the drying in heated mechanical laundry dryers. It has, for example, been proposed to apply on the moist laundry a particulate bleaching agent, which consists of a per-oxygen compound, in particular perborate, and which optionally is present in mixture with an activator, such as tetraacetyl-glycoluril. An essential disadvantage of this process is that the perborate and/or the activator do not spread evenly on the moist fabric, for one thing, because of their relatively low water solubility, so that a uniform bleaching effect is not obtained. Besides, the borate crystals remain on the fabric after the bleaching process, which may be disturbing in use. In another known method, the solid bleaching agent is disposed in a porous container or an open-cell sponge, through the openings of which the bleaching agent is allowed to pass and to act on the textiles to be bleached. Also, with such an arrangement, it may happen that only individual textile portions come in contact with the bleaching agent, in particular, when the container or sponge gets temporarily caught in one of the textile pieces. As the drying process progresses, moreover, the passage from the bleach vehicle to the textile material is made difficult, since because of the lacking water, the perborate crystals no longer dissolve and in solid form do not react with the substrate. Textile portions which come in contact with the bleach vehicle relatively late are, therefore, not bleached or only partially or deficiently so.